Superfluidity

AbstractThis chapter presents a general discussion of the phenomenon of superfluidity, starting from the famous Landau criterion for the critical velocity. The Landau expression for the normal (non-superfluid) component of the gas, expressed in terms of the elementary excitations of the system, is derived. The relationship between Bose–Einstein condensation and the phenomenon of superfluidity is outlined, with special focus on the role played by the phase of the order parameter, whose gradient fixes the velocity of the superfluid. The chapter derives the hydrodynamic equations of superfluids at both zero and finite temperatures and discuss the solutions for first and second sound. The formalism of quantum hydrodynamics is presented, with an application to the Beliaev decay of phonons and to the calculation of the fluctuations of the phase. It also discusses the consequences for superfluidity on the rotational properties and the spatial structure of vortex lines.